GRAYSLAKE MIDDLE SCHOOL

Summer Math Packet

for

Pre-Algebra

Grayslake Middle School  Community Consolidated School District #46 Community Consolidated School District 46 will provide an educational environment that maximizes the potential of all students to be prepared for life’s opportunities while developing a lasting appreciation for learning.

   Dear Parents/Guardians: This booklet has been prepared for students in order to enhance their mathematics skills over the summer months. The open-ended activities involve both skill development and problem solving. While most students should be able to do the pages independently, some students may need your help in developing a work plan and in managing their time. Students are expected to complete the entire packet and return it to school by the Friday of the second full week of school. By fostering a positive approach to the completion of the mathematics packet, you will help your child to learn important math skills and concepts. In addition, your cooperation in assuring that the summer work is completed will contribute to your child’s future success in middle school. Best wishes to you and your family for an enjoyable summer! Sincerely, The Staff of GMS              

 440 N Barron Boulevard  •  Grayslake  •  Illinois  •  60030  •  (847) 223 – 3680  •  FAX 223 – 3526 

 www.d46.k12.il.us

TO ALL STUDENTS: This packet is designed to help you remember the topics that you have covered this past year and to keep the concepts fresh in your mind for the coming school year. You should do a little each week and not wait until the end of the summer to complete the work. It is important for you to know how to do the operations included WITHOUT A CALCULATOR. You must also SHOW ALL OF YOUR WORK! Please take your time and do your best work. There will be time at the beginning the year to ask a few questions, but the majority of the work must be completed before then. This packet is to be turned in to your math teacher no later than the Friday of the second full week of school. This packet is typically one of the first grades of the new school year. Good luck and have a fun summer. See you next year! The GMS Mathematics Teachers

Below are some websites that may assist you in figuring out how to do some of the problem in this packet:

www.aplusmath.com www.math.com

www.mathisfun.com www.aaamath.com

www.purplemath.com (Algebra)

FAQs QUESTION: How will the summer math packets be used when the students return to school? When the students return to school at the end of the summer, we will use these materials as one source to assess learning. Students will receive credit for returning the packet based on guidelines put in place by both the administration and teachers. In addition teachers will assess students based on the packet materials and this assessment will be used to identify needs of the students in the classroom. Most importantly, your son/daughter will have the confidence for the math to be learned in the coming year. QUESTION: What if I don’t know the math or never found math to be my favorite subject? We are asking you to encourage your children to think of themselves as mathematicians who can reason and solve problems. Mathematics is their key to the future. Parents who communicate the importance of mathematics to their children can help them to develop confidence in their own math ability no matter what the comfort level of the parents. We need you to support this packet. QUESTION: Isn’t this a lot to expect in one summer? Do they have to do it all? We do not expect students to do the packet all in one day! Or one sitting? Or the last week? Spread it out over the span of the two summer months. You know your children best. We expect to see a good effort for each student on his or her return. QUESTION: Can’t we have an answer key? We are interested in assessing what our children have actually learned and retained. The packet will be an important tool for the classroom teacher to design lessons appropriate for the needs of the students in each class. Therefore, focus in on the children’s attempting the work to the best of his/her ability. The assessment will tell where the child is, so we really want it to be the student’s work rather than anyone else’s.  

Directions: Please answer the following questions to the best of your abilities. Make sure that you show all of your work when necessary. For all basic calculation problems, DO NOT USE A CALCULTOR. 1) Find the greatest common factor (GCF) of 72,

48, and 36. 2) Find the least common multiple (LCM) of 12,

20, and 24. 3) Find the next three numbers in the pattern:

2, 6, 10, 14, ____, ____, ____ 4) Find the next three numbers in the pattern:

64, 16, 4, ____, ____, ____

EXAMPLE: *Don’t forget the ORDER OF OPERATIONS: Please Excuse My Dear Aunt Sally

The Order of Operations

1. P = Parentheses (perform all operations inside) 2. E = Exponents 3. M/D = Multiplication and Division from left to right 4. A/S = Addition and Subtraction from left to right

€

14 − 3( )2 − 5 ⋅ 2 ÷ 2 = 9( )2 − 5 ⋅ 2 ÷ 2= 81− 5 ⋅ 2 ÷ 2= 81−10 ÷ 2= 81− 5= 76

Perform the indicated operations. 5)

€

2 + 32 − 5

6)

€

6 ⋅ 3− 4 ÷ 2 7)

€

3 4 + 2( ) + 22 −11⋅ 2

8)

€

62 − 3 ⋅ 2 ÷ 5

9) Evaluate

€

3x 2 + 4 if

€

x = 2 . 10) Evaluate

€

−6xy + 2y if

€

x = −2 and

€

y = 3.

Fill in the blanks with <, >, or =. 11)

€

−2____− 7 12)

€

23 ____0.6

EXAMPLE: *When adding and subtracting fractions, you must have a common denominator – use the LCM to find it!

Least Common Multiple of 6 & 8 6: 6, 12, 18, 24, 30, … Once you find the LCM, change each 8: 8, 16, 24, 32, … fraction to it’s equivalent.

€

6 78 + 5 5

6 = 6 7×38×3 + 5 5×4

6×4

= 6 2124 + 5 20

24

=11 4124=11+11724=12 1724

Perform the indicated operations.

13)

€

34

+58

14)

€

516

+316

15)

€

5 25− 358

16)

€

356− 2 79

EXAMPLE: *When multiplying fractions, multiply straight across then simplify. All mixed numbers must be changed to improper fractions. To simplify fractions, find the GCF and divide both the numerator and denominator.

€

2 58 ×

47 = 8×2+5

8 × 47

= 218 ×

47

= 8456

= 84÷2856÷28

= 32

=112

17)

€

5 13⋅ 4 14

18)

€

3 34⋅89

EXAMPLE: *When solving equations, you need to perform the opposite operation. If there are two steps, you need to reverse the order of operations to choose what to do first.

€

3m − 5 = 7 + 5 + 53m =123 3 m = 4

Solve for each variable.

19)

€

4 89

÷ 2 23

= x 20)

€

y =712

÷38

21)

€

4x + 5 = 21

22)

€

3x −12 =15 23)

€

18x = 2 24)

€

−12 =15x

EXAMPLE: *Use the following formulas to help you through percentage problems. The percentage in each formula MUST be converted to DECIMAL form first!

€

Whole ⋅% = Part

€

% =PartWhole

*Use the following formula (same version but with a slight twist in the second one) if you remember how to solve proportion. The percentage in the formula is automatically in percent form.

€

PartWhole

=%100

€

isof

=%100

Solve each word problem making sure that you include units in your final answer when necessary. You may begin to use your calculator here. 25) You’re buying jeans at Kohl’s at 35% off. How much will a $34.98 pair of jeans cost with this sale?

To solve for m, you must get rid of the 3 and 5. Since 3 is being multiplied to m and 5 is being subtracted from it, 5 will be moved first. Use the opposite operation which is addition. You are left with 3 times m which means that you must divide for the opposite operation. Always show division with a “fraction bar.” Simplify to find the final answer.

26) You were taxed $3.12 on a $56 dress. What

was the sales tax percentage? 27) 12% of a school’s student population got sick.

If 92 students are sick, what is the school’s total population?

28) What percent of 48 is 16? 29) 30% of what number is 12? 30) 40% of 250 is what number? 31) If 4 out of 7 students at Johnson High play

sports, about how many of the 504 students at the school play sports?

EXAMPLE: *Use the Means Extremes Property (cross products) to help you solve proportions.

€

ab

=cd

ad = bc

Solve the following proportions.

32)

€

34

=f12

33)

€

3.28

=12m

EXAMPLE: *To convert from fractions to decimals

Divide your fraction (numerator

€

÷ denominator)

€

34 = 3÷ 4 = 0.75

*To convert from fractions to percents Once the denominator becomes 100, the numerator is your percentage

€

45 = 4×20

5×20 = 80100 = 80%

*To convert from decimals to fractions Place your decimal without the decimal point over the place value

€

1.62 =1 62100 =1 3150

*To convert from decimals to percents Simply move your decimal point to the right twice

€

0.003 = 0.3% *To convert from percents to decimals

Simply move your decimal point to the left twice

€

263.2% = 2.632 *To convert from percents to fractions

Place your percentage over 100 and “fix” the fraction so that there are no decimals remaining

€

48.5% = 48.5100 = 485

1000 = 97200

Fill in the following chart.

FRACTION DECIMAL PERCENT

34)

€

23

35)

€

1 34

36)

€

78

37) 1.04

38) 0.7

39) 0.35

40) 7%

41) 127%

42) 0.04%

Solve the following problems with the given formulas. Don’t forget to include units in your answer. 43) Given the radius of a circle is 8.5 mm, find the

area of the circle using

€

A = πr2 to the nearest hundredths.

44) Given a rectangular box with a length of 10 inches, a width of 3 inches, and a height of 4 inches, find the volume of the box (

€

V = lwh ).

45) If the area of a square is 16 squared feet, find

the length of one side (

€

A = s2). 46) The base of a triangle is 6 m long and the height

is 8 m long. Find the area (

€

A = 12 bh ).

47) If the diameter of a circle is 9 cm long, find the

circumference (

€

C = 2πr or

€

C = πd ).

48) Find the area of the trapezoid shown (

€

A = 12 b1 + b2( )h ):

49) Beth’s cookie recipe calls for

€

313

cups of flour and

€

2 23

cups of sugar, which will yield 24 cookies. If she

has 72 friends, how many cups of flour and sugar will she need?

6 m

12 m

20 m

For problems 50-53, use the diagram below.

50) Use a ruler and the scale to find the distance the

boat still needs to travel to dock at Hana Bay (solid line).

51) If the boat did not head towards Hana Bay but remained sailing straight ahead, find the degree of the angle formed between the two “paths” (xo).

52) What location is closest to being 24 miles away

from Skyline Trail? 53) Using the scale, estimate the distance all the

way around the island of Maui.

SCALE

€

14 in = 2 mi

xo

Use the data and graph from question 54 to answer questions 55 & 56. 54) A botanist is experimenting with a new plant fertilizer. She measured the heights of five plants, then

fertilized each plant and measured the plant height again in two weeks. Create a double bar graph below with the data provided. Don’t forget to complete the key as well.

HEIGHT OF PLANT

PLANT Before Fertilizer (cm) After Fertilizer (cm) 1 12.5 17 2 15.5 19.5 3 13.5 17.5 4 18 22.5 5 17.5 23

Plant Height Before and After the Addition of Fertilizer

Hei

ght (

cm)

25

20

15

10

5

0

1 2 3 4 5 Plants

KEY: Height before the addition of fertilizer Height after the addition of fertilizer

55) To the nearest cm, what is the mean increase in height? 56) Which of the five plants increased the most on a percentage basis? By how much did it increase?

EXTENDED RESPONSE QUESTIONS For each of the TWO problems, show all your work. Explain in words how you got your answer and why you did the steps you did to solve the problem. 57) Megan runs 2 miles each day, 5 days a week. She wants to run a marathon, so she asked her coach for some

advice. The coach told Megan that she needs to work herself up to a training routine of 40 miles each week and that she should be running that much for at least 6 weeks prior to the marathon. In addition, the coach told Megan that she should not increase he mileage by more than 10 percent every two weeks. If Megan follows her coach’s advice, in how many weeks can she enter her first marathon?

58) Sole Locker sells new pairs of sneakers for $59.95. This week they are on sale at 10% off plus 6% sales tax. Foot Action sells the same sneakers for $65.50, but this week they are on sale at 18% off plus 6% sales tax. At which store would you pay less for these sneakers and how much would you save?